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Heat capacity measurements of GcS, GcSc and GcTc
~imA'a Acla. 27 (1978) .?~3-231 ~) Els~a~r Sck:ntific Publishing Company. Amsterdam - PHntcd in Tltc Netherlands
H E A T C A P A C I T Y M E A S U R E M E i ~ q ' S O F GcS. GcSc A N D GcTc
H E R I B E R T ~VIEDE.'tlEIF.R.. P A U L S I E ~ t E R S °. U ~ I E S H G A U R A.'~-D
BERNHARD ~ DERLICH ~:mml oy Cllt-m~ry. I~rnxr~!m Pol.rtcrhui¢ ln~imlr. Troy. AYe- }'orL- 121:¢1 ( L.'-5~4.) IIP~__.'~'~_""o~ ~ No~'o~dl~or !9"/7)
ABSTRACT
The heat capacities o f GcS. (3cSc and (3cTc ,vcrc measured in the temperature range 220=610 K , employing a computer interfaced differential scanning calorimeter. Usin~ [ I ~ m~Lsured heat capacily data. the l:)cb~: temperatures o f GcS, GcSc and GcTc ~-crc estimated to be 360, 250 and IS0 K. r ~ p ~ t i v c l y . The I V - V I compounds v,-hh cubic ~ructurc have lo~,~r average force constants than the orthorhombic compounds. The absolute entropies at 29S K ,yore calculated to bc 59.4 :~ 4_0, 71.6 ~ 4.0 and 97.5 -)= 4.0 J K - ' m o l c - ' for G¢S and GcTc, rcspeclivcly. I.%q'RODUCTIOS
C ~ s l a l gro,~lh studies o f GcS, GcS¢ and GeTc by chemical l'apor transport made it necessary to discuss the thermodynamic functions o f these compounds at ~arious temperatures I - J. The heat capacities o f GcS. GcSc and GeTc, hmvcvcr, had not bccn measured in the temperature region o f intcresL This paper presents such heat capacity data in the lempexaturc range 220-610 K- Thc heat capachics arc discussed in terms o f the D e b ~ theta temperatures and the coastal structures. In addition, the absolute entropies o f the C_.crmanium monochalco~enides arc calculated from the hcat capacity data. LSPERIME%'TAL PROC1EDUR~
Heal ca/xlcil)" meas~lremenls
A differential scanning calorimeter (Pcrkin-Elmcr DSC-2) was us~i for the thermal analysis o f all samples. The DSC output xl-as recorded in digital form, suitable for computer evaluation. A detailed dc~ription o f the equipment and computer program is given eb~vhcm ~'. Data points were sampled every 1.2 $ and avcralp:d for heat capacity evaluation. Accuracies better than -~ 0.5% have been
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Fl~. I- ~ c u ~ for Ixmmclin~~tandard ~md ~ ~:lt~ (lWinl-cxtt of d~tta tap¢~)- Lo~+t ctu~-c: Imm:lincroman:middle cubic: mmaptc~can: top cmx~::stan~nJ ~ t n (AI:O~). The Icf~ he~ze~als arc tl~ stagting isothom+, followed by heating from 210 to ~+O K- TI~ ~ t lto6zomal~ arc tl~ c m J ~ ~+mboms. a c h i e ~ t l ,on m e a ~ r e m e n t s ~ i t h z i n c ' . H ~ t i n g ratcs ~ in this w o r k ~ r c i0 K r a i n - ~. T h e sample ~ varied f r o m a b o u t 20 to 60 mE-- T h c me-a~urcmcnts ~ r c o u t u n d e r a flow o f d r y n i t r o ~ n_ Hi oh purity sapphire crystals o f ~ 1 1 k n o w n heat capacity s were cmploycxl as standard_~ T h c tcmpc~raturc r a n ~ o f mc~_~urement was 2_~-610 K. T h e raw d a t a for a ba.~line, ~tandard a n d sample ~z~n consist o f thrcc rc1:ions as shown in Fig. i- Heat capacities am calculated in 10 K in~.rvals. For each calculation, 50 , ~ l a i amplitudcs~ obtained from basdinc, sl~ndard and sample scans are ~ o r d c x l from 5 K bdo~" t o 5 K a b o ~ tlm t e m p e r a t u r e a t w h i c h the h e a t capacity is m e a s u r ¢ ~ A linear lea.~-SClUar~ t r e a t m e n t is p e r f o r m e d o n th e 50 signal amplitud¢:~ a n d a *'flitted'" a m p l i t u d e is calculated at the m e a n t e m p e r a t u r e o f thc m_e-a~-mrcmcnt.+. T h e c~t~poL~tcd baseline a m p l i t u d e ~ subtracted f r o m the " f i t t e d " signal amplitud~ to ~ d ;~n uncorrcctecl dlsplaccmenL T h e u n co rrected displacements a r e calculated every 10 K for baseline, sample a n d s t a n d a r d scans- C o r r e c t e d s t a n d a r d a n d sample a m p l i t u d e s a ~ o b t a i n e d b y subtracting the uncorrected b a . ~ i n e displacements from the u ~ ~and~urd a n d smnple displacements a t each temperature.
Sample preparalion and pan Ioadin.e procedures T h e samples ofGcS,. G e S c a n d G e T e u ~ ! for these sludies were prepared from the e k m c n t s by scaling stoichiomclri¢ quantities o f G e (99.999 ~-~)a n d the c o r r e s p o n d in~. eha!co,-~cn (99-999~/o) in p r e ~ o u s l y cleaned a n d out-~mLs~de fused silica a m p o u l e s at a pr~_+~ure o f 10 - ~ Pa. "i'hc a m p o u l e contents ~ r c a n n e a l e d at 523 K for s ~ r a l hou rs a n d sublimed repeatedly a n d q u a n l i t a l i ~ l y in a n $73 --+ 773 K t e m p e r a t u r e ~radicant. D c b y e - S c h c r r e r X-ray diffraction p h o t o g r a p h s o f the products yielded lattice p a r a m e t e r s for the o r t h o r h o m b i c G c S (a ~- 0.4303 ~ 0.0003 n m. b = 0.3652 0.0003 rim. c ~- !.0449 -~- 0 . 0 ( O rim). for the o r l h o r h o m b i c G e S e (a = 0.4387 ~: 0 . 0 ( O n m . h ---- 0.3837 ~ 0.0006 nm . c -- 1.053 ~ 0.0015 n m ) a n d for the r h o m b o hcdral G e T e (a - 0.5982 ~ 0.0004 n m a n d :z = ~;S.22 ~ 0.2"), in g o o d a o-xccment il ith the literature ~alues. Further dc~ails o f sample p rep aratio n a n d crystal structure ar e reported else~'herc ~" ~. Prior to loading the samples into the a l u m i n u m pans. each c o m p o u n d ~"as dried a n d oulgass,.-'d at 475 K at .~ pressure o f 10 - ~ Pa. T o d e t e r m i n e w h e t h e r thc~c c o m p o u n d s react with a l u m i n u m , GeS, G e S e a n d G c T c , respectively, ~ : r c scaled u n d e r a n a t m o s p h e r e o f desiccated nitrogen in a l u m i n u m pans a n d heated at 8~_.3 K for 2 h- T h e mass o f the sample plus pan r e m a i n e d c o n s l a n t after heating ( ~ t h i n ~ 0.02 mg). Microscopic e x a m i n a t i o n (25:-.'.) o f the o p e n e d pans rc~:aled n o ~ s i b l c rcaclion bct~vccn Ihc samples a n d II1¢ inside o f the a l u m i n u m container. F o r the actual heat capacity runs. all samples ~ r e loaded a n d he, tactically scaled in a l u m i n u m pans in a d r y box c o n t a i n i n g a nitrogen atmosphere. T h e mass o f the po~xlcred sample xx~asd e t e r m i n e d by weighing the pan a n d cover before a n d after loading using a C a h n microbalancc. T h e pans were filled a n d scaled to minimize the free v o l u m e c o n t a i n i n g nitrogen. A t the e nd o f each heat capacity run, the sample plus pa n ~ : r c ~ ' i g h c d to confirm constant mass within e.xperimcotal limits o f error. ItESWL~;
Tlxe heal copacil)~ o f GeS The heat capacity o f G c S ~ s dctermined in the temperature range 220-610 1( and is ~raphically represented in F i ~ ~ A least-squares treatment o f the dam ~elded the e q u a t i o n C'p -- 46.5 ~- I.'49 x 10 - 2 T -- ~01 ~< !0 ~ T --+ (J K - ! mole - 1 )
(I)
•~-hich is valid in the t e m p e r a t u r e range ~_20-5!0 K. T h e heat capacity values for temperatures b e t ~ e e n $20-610 K ~ r c not included in thc least-squares treatment. A n cxothermic thermal effect ~ i t h a n cslimatcd heat o f 105 J m o l e - t x ~ s observed at these temperatures. T h e thermal effect started a t 520 K, a t which t e m p e r a t u r e p r o ~ o u s X-ray diffraclion xludiex revealed a halt in the expansion o f th e crystallographic a- a n d b- axes o f Ge.S ( a b o u t 513 K ) s. Since th e th ermal effect is c-xothermic, ~trqnger b o n d s m a y be f o r m e d d u r i n g the structural changes s a t these temperatures. A further interpretation o f these effects a n d halt in the thermal expansion is n o t
226
..1
I "
-
"..,-'3"-
!
"
Temper(afore ( K ) Fig. ~ ~ ~ It~l CalX~cityx+:llu~ of ~ ~ I¢~st-~qwr¢~ fit i t ~ l c+pocity functio~ for G
and C~Tc ~ ~tfunction of tonpo-~tur¢- "l'hc and (icTc arc _ r c p r c ~ l d ;t~ sold lines.
justified hosed o n prcscnt d a t a . T h e " f i t t e d curve'" r c p r c s c n t c d by" c q n . ( I ) is p l o t t c d i n R ~ . Z T h e s t a n d a r d d ~ v i a t i o n o f t h e d a t a is A 0_! J K - w m o l e - s_ The m a x i m u m d c ~ a t i o n o f t h e h e a t c a p a c i t y x~lucs from cqn_ ( ! ) is ~- 0_5~C.
The h ~ t ~lmCill" o f Gc.~" The heat capacity o f C J ~ c x~-asmcasurod in the Icmpc~turc ran~o¢ ?.20-610 K in thro~ runs_ The ~ l t s ar~ graphically rcpre~ntod in Fio_. ! A Icast-~luarcs a r l a l ~ s Of the data ~cldcd the following heat capacity, function o f GcSc Cp = 50.2 + 9.60 :< I0 - J T - -
!_$7 ~< 10 ~ T - : (J K - ° m o l e - ' )
(2)
which is also shown in F i ~ 2. Tltc maximum dcviation o f the heat capacity ~,~alucs from cqn. (2) is ~. 1 . 5 ~ and the stand=rd deviation o f the data is ~ 0.4 J K mole- '. N o unusual thermal effects wcrc o~Nscrvcd in the Ge.Sc hcat capacity data which is consistent with the thermal expansion sial-dies"~.
The h ~ t cupacity o f GcTc The Igat capacity o f CgTc ,,-as ngasurcd in lhc tCmlgraturc r a n ~ 220-460 K in t ~ o runs. Thc data arc ~t-aphically r c p ~ t c d in R ~ ~ A linear Icast-~luarcs anal'sis o f lhc data yicldod the exp _rcs__~on Cp = 45;.9 -~- ?7-22 :< I 0 - " T ( J K - '
molc- ')
(3)
which Fgod~ts thc hcat capacity o f C~Tc v,ithin :. !.6.";~ in lhc lcmpcgaturc ran~c ~50 K. "l'hc standard d ~ t i o n o f the data i~ -~ 0_:5J K - I mole- i_ The -j-aphical rcprcscnlation o f the equation is includ~l in R ~ 2 as a linear plot lhrouo_h thc GcTc heat c a p a c i t y d a t a .
The calculalian o f Beb)'e temperalures Art the I:)cb~c tcmpcvaturc C~ has r c a c h ~ about 95~z. o f its limiting value.. For
227 TABLE
I
T i e DtW~'~Te3at,tu~r~tt~ o r GcS. Gc~>c a,_~r~GcT¢ C,u.~L,'L~'r~D [ttou Tam~'t.,vno_~ o f D(.0t,~iT)x_~
T
Cp
C,
C,~6R
(K)
I J K-I nmlv~*)
(J K ~ n~e-')
DfO~7-I
45.61 46-1 t
0.$63s 0.b-704 0-~62
46-99
43-09 43-42 43.71 43.95
4:~-47 4S-~%'9
45-65 45~
-~I9-27
46.09
49-62
GeS "~-,o 240
O~T
Oo (K)
I~ 1-6135
382 3s9 396 403
1.34-12 i-303:g I ~-2t~3
300 30.11
46.26
0-9 ! 5 i 0-9!99 0-9239 0.9273
I ~.2379
309
Y,0.S2 $1941 5t ~.26
47-S9 .I-/.95 4SJI)I
0.geo0 0.9612 0.9624
0_90"F,__ 0-8931 0.gT~2
2X10 205 211
$ i .4S
4~:-07
0.9636
0-.~634
2 i6
46-57
0-.~ IO
1.731;I 1-6911
Ge.~" 240 Gc-7"c-
240
~
~
in U!g l-.c~! capacity i'~lucs h ~ only calcutationa! si.lmi~canc~
b i n a r y c o m p o u n d s w i t h 2 a t o n ~ p e r m o l e c u l e , t h e l i m i t i n g v a l u e o f C~ is 6 R -~ 50 J K- t mole- t U s i n g t h e l e a s t - s q u a r e e_xpre~iorL~ f o r G c S . G c S e a n d G c T e . ( e q n s . I - 3 ) , C D • ~alucs x,~-e c a l c u l a t e d a t 220, 230, 240, a n d 250 K f o r t h e t h r e e c o m p o u n d s . T h e v a l u e s o f C , f o r G c 5 , G C ~ a n d G e T c m~rc c ~ t i m a t c d f r o m t h e Cp ~alucs usinf, t h e N e r n s t and Lindcmann 9 approximation
c,
-
-
AoC77T=
(4)
~-here T _ i~ t h e m e l t i n g p o i n t o f t h e solid a n d -4o is a u n i v e r s a l c o n s t a n t e q u a l t o 5_12 ~ 10 - ~ J K - t m o l e - t. T h e m e l t i n g p o i n t s o f 931 K t ° . 948 K t t a n d 996 K t z h a v e b e e n r e p o r t e d f o r G e S . G e S e a n d GcT-e.. respectively. T h e r e s u l t s o f t h c ~ calculatiorL~ a r e s h o w n in T a b l e I. It is c-,ident f r o m T a b l e I l h a l l h e C. x~tluc~ f o r Gee at temperatures bet~:~n ~ and ~ K are greater than 47 J K-t mole-t ( 6 R :-.~ 0.95) a s c o m p a r e d t o t h e C,~ v a l u e s f o r G c S a n d Ge.Sc w h i c h a r e less t h a n 4 7 J K - t m o l e - '. T h e s e r e s u l t s i n d i c a t e t h a t t h e D c b y e t e m p e r a t u r e , 0 o, f o r G e T ¢ is b e l o w 220 K , w h e r e a s t h c 0 o valuc~ f o r G c S a n d G c ~ arc: ~orcatcr t h a n 250 K. T o c o m p u t e 0 o f o r G e S . G e S e a n d G c T e , t h e r a t i o C J 6 R u,~as c a l c u l a t e d f o r e a c h c o m p o u n d a t 2_'20 t o ~ K. T h e d i m e x t s i o n l ~ r a t i o C d 6 R is e q u a l t o D { 0 J 7 " ) ,
the Debye funclion for binary compounds 0o
[x = h,/kTJ Using a tabulation o f I I ~ Debye function ~~, values o f Op Ii~rc calculat©d at the four tcmpctaturc.~ G~q~.'rally. heat c a p ~ c i t y dctcrminations at lower tcmpcraturc~ arc m o r c rcliab!c for l l ~ calculation o f 0 o Ibex=use C. has a ~ t e r temperature del~ndenc~ at l o ~ r tcml)cratures and ¢ffccts o f anharmonicity arc s m l l c r . With this fact in mind. the trends in thc 0n values for C~-S. GcSc and GcTc as a function o f tcmpcraturc 5ug~st that estimated 0o values arc about 360. 284) and I SO K for GcS, GcSc and C~Tc, ~ ~ c ~ . Thc 0 o value o f I SO K for G,=Tc can Ix: compar~l t o a r q ) o r t ~ l value o f If~) K based on low temp,~raturc heat capacity measurements |= in the ran.~c 0 . I - I . I K . T I ~ [:)~ye teml~raturc for GeTe is the low~;t o f the t h r ~ compounds studi~l in this work and must I ~ the least accurate from our rc!ativcly high tcmpcraturc m ~ ~ t s . In vicw o f this, thc a_mrccmcnt ~ i l h the result obtained at the l o ~ r temperaturc l'~ is gralifyin~ It furthexmorc indicates that no low tempcraturc complications sccm to exist in thc hcat capacitics. TABLE
2
~
"IIE34rlEI~llJ1tlE. ~
Co,~mm~
( o n e ) Cx:Te (ml~bic)
(ormo,hon~k:) ~,T¢ (c.i~) Pr~
(col,k:) ]PIbTc
(cut,~)
IFii[~L~Lq,X~. E [ I ~ ' C I [ D ~
A_~q) A~,-DLa~I~ faRCl~ ('T~STA~,'r OF Iv,,-'~,l
OD ( Jk')
rD
p
A r c r ~ e force const~mt
36O ~ 20
7-50
3-69
SI-9
2SO ~ 2O
5-S3
6--'-S
,54.3
!66 ~ 3w~
3.46
7.(~
36-3
~
5-63
4-19
$~_-4
210~
4-.~
7.S7
:~
(SO) 1401" (--)
~92-
_-~r7|:
4_-J~
4-61
40-7
13~ ~
~
9-49
31-0
I??,.~W=
~.~
_.('z~__)
(mJ)
IO~
34-3
C"J)O)
("Jim
= ( ) hxlk:atc5 tcmpe:~turc OR) at which ten ~
6 : ~ ~ _
13-1
35-1
229 T h e vibration frequency o f a solid can Ix: related to a n averagc force constant, B, a n d the reduced mass,/s, o f thc vibrating a t o m s by the equation % -
~
(6)
T h e reduced mass can Ix: calculated f r o m the M. I~ =
M.
cxprcmion
x Mc ÷ M,:
( 7)
where M , , and M¢ arc the masses o f the metal and chalco~n atoms, respectively. Using the 0 o values for GcS and ~ determined in these studies and the 0 o value o f 166 ~; 3 K for (3¢Tc I"~, the a,,~ra~c force constants for these compounds v,-crc calculated. Additionally. literature 0o values for the tin t ~- t 6 and lead w"~chalcogJmides wcrc used to calculate thc avcra~.c force constants o f thcsc compounds. Table 2 fists the Dcbyc t c m l ~ r a t u r ~ , IE)cb~-e frequencies, reduced masses and avcragc force constants for the above I V - V I binary compounds- It can be so~n from Table 2 that the 0t) values d c ~ . ~ with increasing atomic weight o f the chalcogen and o f the metal atoms in this s~ries_ The average force constants o f the metal chalcogenides arc apparently a function o f crystal structure. For the orthorhombic compounds (C;eS, Gc.S~ SnS, SnSc), the average force constant is hi~hcr than for the c,,bic o r rhombohodral structure. The B ~-alues for the orthorhombic compounds are nearly t~vice as large as those for the cubic compounds in this series. The obscr~'ation that the B values for Ge.S and OcS~ arc about cqual sug~csts that thc lower 0 o valuc for ~ is mainly a result o f increased molecular weight and not o f binding differences within the respective solids. Similar conclusions may bc drawn concerning other I V - V [ comp o u n d s with similar B values. Ttm rather large difference in the average force constants bet~n the orthorhombic and cubic IV-VI c o m p o u n d s is probably due to the complex nature o f the orthorhombic structure as compared to thc hi o-.h|y symmetrical NaCl-typc structurc.
The calculation o f ahsoht[e entropies from/teat capacity data T h e Debye function m a y be used to predict the absolutc e n t r o p y o f a c o m p o u n d according to the equation -~-
= 3
(s)
XVe used cqn. (8) to calculatc the absolute entropy o f the ~oermanium chalco~enides at 2--'0 K and the h ~ t capacity functions as measured in these studies to obtain the absolute entropy 3"~.o= for the compounds. From tabulations ~~ ofeqn. (8) and the 0t) valucs o f GcS and GeSc, the abso!utc cntroD- at ?.20 K is 45.2 and :56.5 J K - z mole- ' for GcS and GeSc, respectively_ !ntc~.~rating the heat capacity functions o f Cw.S a n d GeSe from ?.20 to 298 K yields additional e n t r o p y changes o f 14.2 a n d 15.1 J K - ! m o l e - t respectively. T h e absolute
c n t r o p i ~ S~'~s for G e S a n d GeSe arc thus 59.4 ~ 4.0 a n d 71.6 ~: 4.0 J K - ' m o l e - ' rcspeclix~ly. T h e error limits o f ~: 4.0 J K " s mole arc estimated from the 20 K uncertainIy in Ihc 01~ ,,-alucs used to calculate the cntroi~- at "r~__0K. T h e calculation o f S~., s for GcTc is based o n a sorn~t-hat different procedure. Using the 0~, ~ l u c o f 166 ~ 3 K ' * 1he absolute entropy k calculated at 166 K. It is a.~,sumed that o u r G e T c heat capacity funclion [cqn. ( 3 ) ] is ~-a!id from 166~29~ K although the h ~ t capacity xx~ actually measured from "220--4~ K. At 166 K the absolute cxtlropy o f GcTc is 67.8 J K - ~ nsok~ a n d integrating the m_,~_~ured heat c:tpadly -,dd.~ a n additional e n t r o p y chan~e o f 29_7 J IC - s m o l e - * from 166 to 295 K tO ~ e l d 5~.,~s = 97.5 -~ 4.0 J K - s m o l ~ - s for GeTc. A .similar calculalion ba~:d o n the Or, value o f !50 ~ 20 K for G e T e yields ~,~s = 93_7 ~_~4.0 J K - s m o l e - ~ which is m~lhin error l i m i ~ o f the absolute ~rllropy ~-alu¢ oblained using the 0 o x~lluc o f 166 IC. SUMMARY A ~ D CO.'~CI.la~IO.~C~_
As a result o f heat capacity mcasurcmcnls on GeS GcS~ a n d GcTe in the temperature range 220--610 K. 0o ~ l u e s and average force constanls. B. were calculated for the~,e materials a n d com!~-.~cd t o other IV-V! compounds_ It is observed that th~ ma~nitudc o f t lw. B values d c l ~ n d s upon the crystal structure_ T h e absolute entropies at 298 K wcrc calculated to be ~9.4 _-~ 4.0. 7 !.6 .~ 4.0 a n d 97.5 ~ 4.0 J K - a m o l e - t for GeS. GeS~ a n d G c T ~ rcs.ncctK~ly. T h c ~ x~alucs arc in c l o ~ aZ-.rcera~nt w h h absolute ~ r l t r o u ~ cakula(~.'~ independently from K n u d s e . n - t ~ •-aporization studicy,, namely, 58.6 - 6. 70.8 - 8 and 94.6 :~ 8 J K - ~ m o l e - ' for G¢~ '~, Gc.Sc s'~ a n d GeTc ze. rcspccli~'cly. A ~hcrmal effect at 5"0 K o ~ ¢ r v c d in ~be heal capacity m c a ~ u ~ t s o f GcS corrcspondL~ Io a halt in the thermal expansion o f the a- and b-axes observed in high Kempcratur¢ X-ray diffraction ~tudies': o f this c o m p o u n d .
T h e ~ u t h o ~ arc p ~ to acknowledge the support o f this work in part by the National Science F o u n d a t i o n and by t!~ National Aeronautics and Space Administration. REFIERE~CI~ I 2 3 4 5 6 7 &
}l. XV'~cl~-i~r. E A, I r ~ ;and A- K - C h ~ u d h u n . J . Cry,JI. Gnm'~h. 13~!4 (19T2) 393H . VCk'dcmcicr and E A - I r c ~ . Z . . 4 ~ . AII~. Ch~'m~ ~ {19T31 59}1. X V k x J ~ a n d P. A- ~ m ' ~ , . Ko ! ~ p u b l ~ _ U . ~ m r , A- ~ | c h l a ~ m ~ l B . ~ V ~ h . J . ~ - A m ~ / - , 13t!97S171. D.C-G~ningsamdG-T. Fumud~l..J-Am'-C/aem-.~c'-7$KIg-~3}5 "~ilL. ~,Vicdc~nmcicr and A- G- S~u~ai.J. C r~c~r. Grs~m~b. 6 {196~) 67. H - xV-acdm~icr and P. A- ~ 7.- A~w~. AI~_ Cl~m~ 41 i 119751 ~10_ X - v ~ V k ~ m c i c r a n d P. A - .5~cmcrs. Z - .4nmT- AIlff. Clwm.. 431 (197"/) _-"99.
231 9 XV. N a n s l and F. A. L i n d a n a n n . ~ - FJe'ktr~clwm.. 17 (191 I ) SI7. 10 W . Y i g ~ c ~nd G- ~|oh. ~Xr4~'~]ad~rb_ . t S i ~ r L d . . . l l m ~ l ~ . . 6 (19T0) ~ 3 . I I !_. R x ~ and NI. Bour~a:m. C(m. J. Clam:-. 47 (:'~k~) 2-55512 J . P . ~IcHu~h ;~nd XV. A. Ti!!cr. Trine..41AII~ 21; (1960) I g ~ 13 G- T- Fm~ska,= and T. B. ~ in D. E- Gr:sy (EJ_)..-l,wric~mInslil~le,~Phr~irs llamlbouk. NlcGr-J~'-Hill.~ " York. 195"/.pp. 4-! !2. 14 L- F i m ~ x ~ . Pb~. ~-r./.~I-. I~ ~:o. 7 (!96J) ?_13_ IS P.V. Gult~c~" and A- V. Pctro~. ~or. Pb~s. ~I~I State, I (1959) 3.~0. 16 D. H- l ~ n ~ L , C- R. N;grlin and R- C- .~!i!~';-.. J- .-t/,~l_/'~s-x_34 (19~3) .',01~.;. 17 P. Aig~dn a n d M. Bulkauski. 5¢l~t'l~d Comloulx R d o t i r r to .~micordt~rar~. P c r ~ n ~ n i ~ r ¢ ~ 196!. I~ El. ~ . V ' ~ - r a n d P- A- ~ ' m o ~ . t o b c p u b l ~ h c d . 19 H - XV'~Ac,m c i ~ a n d I~. A- Irct~., Z..4nor~...lllg. Clan'... 404 (1974) _~]pg. 20 H- X V ' ~ a n d F- C- KL~x~s;~_work in pr.ogrcss.
H E A T C A P A C I T Y M E A S U R E M E i ~ q ' S O F GcS. GcSc A N D GcTc
H E R I B E R T ~VIEDE.'tlEIF.R.. P A U L S I E ~ t E R S °. U ~ I E S H G A U R A.'~-D
BERNHARD ~ DERLICH ~:mml oy Cllt-m~ry. I~rnxr~!m Pol.rtcrhui¢ ln~imlr. Troy. AYe- }'orL- 121:¢1 ( L.'-5~4.) IIP~__.'~'~_""o~ ~ No~'o~dl~or !9"/7)
ABSTRACT
The heat capacities o f GcS. (3cSc and (3cTc ,vcrc measured in the temperature range 220=610 K , employing a computer interfaced differential scanning calorimeter. Usin~ [ I ~ m~Lsured heat capacily data. the l:)cb~: temperatures o f GcS, GcSc and GcTc ~-crc estimated to be 360, 250 and IS0 K. r ~ p ~ t i v c l y . The I V - V I compounds v,-hh cubic ~ructurc have lo~,~r average force constants than the orthorhombic compounds. The absolute entropies at 29S K ,yore calculated to bc 59.4 :~ 4_0, 71.6 ~ 4.0 and 97.5 -)= 4.0 J K - ' m o l c - ' for G¢S and GcTc, rcspeclivcly. I.%q'RODUCTIOS
C ~ s l a l gro,~lh studies o f GcS, GcS¢ and GeTc by chemical l'apor transport made it necessary to discuss the thermodynamic functions o f these compounds at ~arious temperatures I - J. The heat capacities o f GcS. GcSc and GeTc, hmvcvcr, had not bccn measured in the temperature region o f intcresL This paper presents such heat capacity data in the lempexaturc range 220-610 K- Thc heat capachics arc discussed in terms o f the D e b ~ theta temperatures and the coastal structures. In addition, the absolute entropies o f the C_.crmanium monochalco~enides arc calculated from the hcat capacity data. LSPERIME%'TAL PROC1EDUR~
Heal ca/xlcil)" meas~lremenls
A differential scanning calorimeter (Pcrkin-Elmcr DSC-2) was us~i for the thermal analysis o f all samples. The DSC output xl-as recorded in digital form, suitable for computer evaluation. A detailed dc~ription o f the equipment and computer program is given eb~vhcm ~'. Data points were sampled every 1.2 $ and avcralp:d for heat capacity evaluation. Accuracies better than -~ 0.5% have been
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Fl~. I- ~ c u ~ for Ixmmclin~~tandard ~md ~ ~:lt~ (lWinl-cxtt of d~tta tap¢~)- Lo~+t ctu~-c: Imm:lincroman:middle cubic: mmaptc~can: top cmx~::stan~nJ ~ t n (AI:O~). The Icf~ he~ze~als arc tl~ stagting isothom+, followed by heating from 210 to ~+O K- TI~ ~ t lto6zomal~ arc tl~ c m J ~ ~+mboms. a c h i e ~ t l ,on m e a ~ r e m e n t s ~ i t h z i n c ' . H ~ t i n g ratcs ~ in this w o r k ~ r c i0 K r a i n - ~. T h e sample ~ varied f r o m a b o u t 20 to 60 mE-- T h c me-a~urcmcnts ~ r c o u t u n d e r a flow o f d r y n i t r o ~ n_ Hi oh purity sapphire crystals o f ~ 1 1 k n o w n heat capacity s were cmploycxl as standard_~ T h c tcmpc~raturc r a n ~ o f mc~_~urement was 2_~-610 K. T h e raw d a t a for a ba.~line, ~tandard a n d sample ~z~n consist o f thrcc rc1:ions as shown in Fig. i- Heat capacities am calculated in 10 K in~.rvals. For each calculation, 50 , ~ l a i amplitudcs~ obtained from basdinc, sl~ndard and sample scans are ~ o r d c x l from 5 K bdo~" t o 5 K a b o ~ tlm t e m p e r a t u r e a t w h i c h the h e a t capacity is m e a s u r ¢ ~ A linear lea.~-SClUar~ t r e a t m e n t is p e r f o r m e d o n th e 50 signal amplitud¢:~ a n d a *'flitted'" a m p l i t u d e is calculated at the m e a n t e m p e r a t u r e o f thc m_e-a~-mrcmcnt.+. T h e c~t~poL~tcd baseline a m p l i t u d e ~ subtracted f r o m the " f i t t e d " signal amplitud~ to ~ d ;~n uncorrcctecl dlsplaccmenL T h e u n co rrected displacements a r e calculated every 10 K for baseline, sample a n d s t a n d a r d scans- C o r r e c t e d s t a n d a r d a n d sample a m p l i t u d e s a ~ o b t a i n e d b y subtracting the uncorrected b a . ~ i n e displacements from the u ~ ~and~urd a n d smnple displacements a t each temperature.
Sample preparalion and pan Ioadin.e procedures T h e samples ofGcS,. G e S c a n d G e T e u ~ ! for these sludies were prepared from the e k m c n t s by scaling stoichiomclri¢ quantities o f G e (99.999 ~-~)a n d the c o r r e s p o n d in~. eha!co,-~cn (99-999~/o) in p r e ~ o u s l y cleaned a n d out-~mLs~de fused silica a m p o u l e s at a pr~_+~ure o f 10 - ~ Pa. "i'hc a m p o u l e contents ~ r c a n n e a l e d at 523 K for s ~ r a l hou rs a n d sublimed repeatedly a n d q u a n l i t a l i ~ l y in a n $73 --+ 773 K t e m p e r a t u r e ~radicant. D c b y e - S c h c r r e r X-ray diffraction p h o t o g r a p h s o f the products yielded lattice p a r a m e t e r s for the o r t h o r h o m b i c G c S (a ~- 0.4303 ~ 0.0003 n m. b = 0.3652 0.0003 rim. c ~- !.0449 -~- 0 . 0 ( O rim). for the o r l h o r h o m b i c G e S e (a = 0.4387 ~: 0 . 0 ( O n m . h ---- 0.3837 ~ 0.0006 nm . c -- 1.053 ~ 0.0015 n m ) a n d for the r h o m b o hcdral G e T e (a - 0.5982 ~ 0.0004 n m a n d :z = ~;S.22 ~ 0.2"), in g o o d a o-xccment il ith the literature ~alues. Further dc~ails o f sample p rep aratio n a n d crystal structure ar e reported else~'herc ~" ~. Prior to loading the samples into the a l u m i n u m pans. each c o m p o u n d ~"as dried a n d oulgass,.-'d at 475 K at .~ pressure o f 10 - ~ Pa. T o d e t e r m i n e w h e t h e r thc~c c o m p o u n d s react with a l u m i n u m , GeS, G e S e a n d G c T c , respectively, ~ : r c scaled u n d e r a n a t m o s p h e r e o f desiccated nitrogen in a l u m i n u m pans a n d heated at 8~_.3 K for 2 h- T h e mass o f the sample plus pan r e m a i n e d c o n s l a n t after heating ( ~ t h i n ~ 0.02 mg). Microscopic e x a m i n a t i o n (25:-.'.) o f the o p e n e d pans rc~:aled n o ~ s i b l c rcaclion bct~vccn Ihc samples a n d II1¢ inside o f the a l u m i n u m container. F o r the actual heat capacity runs. all samples ~ r e loaded a n d he, tactically scaled in a l u m i n u m pans in a d r y box c o n t a i n i n g a nitrogen atmosphere. T h e mass o f the po~xlcred sample xx~asd e t e r m i n e d by weighing the pan a n d cover before a n d after loading using a C a h n microbalancc. T h e pans were filled a n d scaled to minimize the free v o l u m e c o n t a i n i n g nitrogen. A t the e nd o f each heat capacity run, the sample plus pa n ~ : r c ~ ' i g h c d to confirm constant mass within e.xperimcotal limits o f error. ItESWL~;
Tlxe heal copacil)~ o f GeS The heat capacity o f G c S ~ s dctermined in the temperature range 220-610 1( and is ~raphically represented in F i ~ ~ A least-squares treatment o f the dam ~elded the e q u a t i o n C'p -- 46.5 ~- I.'49 x 10 - 2 T -- ~01 ~< !0 ~ T --+ (J K - ! mole - 1 )
(I)
•~-hich is valid in the t e m p e r a t u r e range ~_20-5!0 K. T h e heat capacity values for temperatures b e t ~ e e n $20-610 K ~ r c not included in thc least-squares treatment. A n cxothermic thermal effect ~ i t h a n cslimatcd heat o f 105 J m o l e - t x ~ s observed at these temperatures. T h e thermal effect started a t 520 K, a t which t e m p e r a t u r e p r o ~ o u s X-ray diffraclion xludiex revealed a halt in the expansion o f th e crystallographic a- a n d b- axes o f Ge.S ( a b o u t 513 K ) s. Since th e th ermal effect is c-xothermic, ~trqnger b o n d s m a y be f o r m e d d u r i n g the structural changes s a t these temperatures. A further interpretation o f these effects a n d halt in the thermal expansion is n o t
226
..1
I "
-
"..,-'3"-
!
"
Temper(afore ( K ) Fig. ~ ~ ~ It~l CalX~cityx+:llu~ of ~ ~ I¢~st-~qwr¢~ fit i t ~ l c+pocity functio~ for G
and C~Tc ~ ~tfunction of tonpo-~tur¢- "l'hc and (icTc arc _ r c p r c ~ l d ;t~ sold lines.
justified hosed o n prcscnt d a t a . T h e " f i t t e d curve'" r c p r c s c n t c d by" c q n . ( I ) is p l o t t c d i n R ~ . Z T h e s t a n d a r d d ~ v i a t i o n o f t h e d a t a is A 0_! J K - w m o l e - s_ The m a x i m u m d c ~ a t i o n o f t h e h e a t c a p a c i t y x~lucs from cqn_ ( ! ) is ~- 0_5~C.
The h ~ t ~lmCill" o f Gc.~" The heat capacity o f C J ~ c x~-asmcasurod in the Icmpc~turc ran~o¢ ?.20-610 K in thro~ runs_ The ~ l t s ar~ graphically rcpre~ntod in Fio_. ! A Icast-~luarcs a r l a l ~ s Of the data ~cldcd the following heat capacity, function o f GcSc Cp = 50.2 + 9.60 :< I0 - J T - -
!_$7 ~< 10 ~ T - : (J K - ° m o l e - ' )
(2)
which is also shown in F i ~ 2. Tltc maximum dcviation o f the heat capacity ~,~alucs from cqn. (2) is ~. 1 . 5 ~ and the stand=rd deviation o f the data is ~ 0.4 J K mole- '. N o unusual thermal effects wcrc o~Nscrvcd in the Ge.Sc hcat capacity data which is consistent with the thermal expansion sial-dies"~.
The h ~ t cupacity o f GcTc The Igat capacity o f CgTc ,,-as ngasurcd in lhc tCmlgraturc r a n ~ 220-460 K in t ~ o runs. Thc data arc ~t-aphically r c p ~ t c d in R ~ ~ A linear Icast-~luarcs anal'sis o f lhc data yicldod the exp _rcs__~on Cp = 45;.9 -~- ?7-22 :< I 0 - " T ( J K - '
molc- ')
(3)
which Fgod~ts thc hcat capacity o f C~Tc v,ithin :. !.6.";~ in lhc lcmpcgaturc ran~c ~50 K. "l'hc standard d ~ t i o n o f the data i~ -~ 0_:5J K - I mole- i_ The -j-aphical rcprcscnlation o f the equation is includ~l in R ~ 2 as a linear plot lhrouo_h thc GcTc heat c a p a c i t y d a t a .
The calculalian o f Beb)'e temperalures Art the I:)cb~c tcmpcvaturc C~ has r c a c h ~ about 95~z. o f its limiting value.. For
227 TABLE
I
T i e DtW~'~Te3at,tu~r~tt~ o r GcS. Gc~>c a,_~r~GcT¢ C,u.~L,'L~'r~D [ttou Tam~'t.,vno_~ o f D(.0t,~iT)x_~
T
Cp
C,
C,~6R
(K)
I J K-I nmlv~*)
(J K ~ n~e-')
DfO~7-I
45.61 46-1 t
0.$63s 0.b-704 0-~62
46-99
43-09 43-42 43.71 43.95
4:~-47 4S-~%'9
45-65 45~
-~I9-27
46.09
49-62
GeS "~-,o 240
O~T
Oo (K)
I~ 1-6135
382 3s9 396 403
1.34-12 i-303:g I ~-2t~3
300 30.11
46.26
0-9 ! 5 i 0-9!99 0-9239 0.9273
I ~.2379
309
Y,0.S2 $1941 5t ~.26
47-S9 .I-/.95 4SJI)I
0.geo0 0.9612 0.9624
0_90"F,__ 0-8931 0.gT~2
2X10 205 211
$ i .4S
4~:-07
0.9636
0-.~634
2 i6
46-57
0-.~ IO
1.731;I 1-6911
Ge.~" 240 Gc-7"c-
240
~
~
in U!g l-.c~! capacity i'~lucs h ~ only calcutationa! si.lmi~canc~
b i n a r y c o m p o u n d s w i t h 2 a t o n ~ p e r m o l e c u l e , t h e l i m i t i n g v a l u e o f C~ is 6 R -~ 50 J K- t mole- t U s i n g t h e l e a s t - s q u a r e e_xpre~iorL~ f o r G c S . G c S e a n d G c T e . ( e q n s . I - 3 ) , C D • ~alucs x,~-e c a l c u l a t e d a t 220, 230, 240, a n d 250 K f o r t h e t h r e e c o m p o u n d s . T h e v a l u e s o f C , f o r G c 5 , G C ~ a n d G e T c m~rc c ~ t i m a t c d f r o m t h e Cp ~alucs usinf, t h e N e r n s t and Lindcmann 9 approximation
c,
-
-
AoC77T=
(4)
~-here T _ i~ t h e m e l t i n g p o i n t o f t h e solid a n d -4o is a u n i v e r s a l c o n s t a n t e q u a l t o 5_12 ~ 10 - ~ J K - t m o l e - t. T h e m e l t i n g p o i n t s o f 931 K t ° . 948 K t t a n d 996 K t z h a v e b e e n r e p o r t e d f o r G e S . G e S e a n d GcT-e.. respectively. T h e r e s u l t s o f t h c ~ calculatiorL~ a r e s h o w n in T a b l e I. It is c-,ident f r o m T a b l e I l h a l l h e C. x~tluc~ f o r Gee at temperatures bet~:~n ~ and ~ K are greater than 47 J K-t mole-t ( 6 R :-.~ 0.95) a s c o m p a r e d t o t h e C,~ v a l u e s f o r G c S a n d Ge.Sc w h i c h a r e less t h a n 4 7 J K - t m o l e - '. T h e s e r e s u l t s i n d i c a t e t h a t t h e D c b y e t e m p e r a t u r e , 0 o, f o r G e T ¢ is b e l o w 220 K , w h e r e a s t h c 0 o valuc~ f o r G c S a n d G c ~ arc: ~orcatcr t h a n 250 K. T o c o m p u t e 0 o f o r G e S . G e S e a n d G c T e , t h e r a t i o C J 6 R u,~as c a l c u l a t e d f o r e a c h c o m p o u n d a t 2_'20 t o ~ K. T h e d i m e x t s i o n l ~ r a t i o C d 6 R is e q u a l t o D { 0 J 7 " ) ,
the Debye funclion for binary compounds 0o
[x = h,/kTJ Using a tabulation o f I I ~ Debye function ~~, values o f Op Ii~rc calculat©d at the four tcmpctaturc.~ G~q~.'rally. heat c a p ~ c i t y dctcrminations at lower tcmpcraturc~ arc m o r c rcliab!c for l l ~ calculation o f 0 o Ibex=use C. has a ~ t e r temperature del~ndenc~ at l o ~ r tcml)cratures and ¢ffccts o f anharmonicity arc s m l l c r . With this fact in mind. the trends in thc 0n values for C~-S. GcSc and GcTc as a function o f tcmpcraturc 5ug~st that estimated 0o values arc about 360. 284) and I SO K for GcS, GcSc and C~Tc, ~ ~ c ~ . Thc 0 o value o f I SO K for G,=Tc can Ix: compar~l t o a r q ) o r t ~ l value o f If~) K based on low temp,~raturc heat capacity measurements |= in the ran.~c 0 . I - I . I K . T I ~ [:)~ye teml~raturc for GeTe is the low~;t o f the t h r ~ compounds studi~l in this work and must I ~ the least accurate from our rc!ativcly high tcmpcraturc m ~ ~ t s . In vicw o f this, thc a_mrccmcnt ~ i l h the result obtained at the l o ~ r temperaturc l'~ is gralifyin~ It furthexmorc indicates that no low tempcraturc complications sccm to exist in thc hcat capacitics. TABLE
2
~
"IIE34rlEI~llJ1tlE. ~
Co,~mm~
( o n e ) Cx:Te (ml~bic)
(ormo,hon~k:) ~,T¢ (c.i~) Pr~
(col,k:) ]PIbTc
(cut,~)
IFii[~L~Lq,X~. E [ I ~ ' C I [ D ~
A_~q) A~,-DLa~I~ faRCl~ ('T~STA~,'r OF Iv,,-'~,l
OD ( Jk')
rD
p
A r c r ~ e force const~mt
36O ~ 20
7-50
3-69
SI-9
2SO ~ 2O
5-S3
6--'-S
,54.3
!66 ~ 3w~
3.46
7.(~
36-3
~
5-63
4-19
$~_-4
210~
4-.~
7.S7
:~
(SO) 1401" (--)
~92-
_-~r7|:
4_-J~
4-61
40-7
13~ ~
~
9-49
31-0
I??,.~W=
~.~
_.('z~__)
(mJ)
IO~
34-3
C"J)O)
("Jim
= ( ) hxlk:atc5 tcmpe:~turc OR) at which ten ~
6 : ~ ~ _
13-1
35-1
229 T h e vibration frequency o f a solid can Ix: related to a n averagc force constant, B, a n d the reduced mass,/s, o f thc vibrating a t o m s by the equation % -
~
(6)
T h e reduced mass can Ix: calculated f r o m the M. I~ =
M.
cxprcmion
x Mc ÷ M,:
( 7)
where M , , and M¢ arc the masses o f the metal and chalco~n atoms, respectively. Using the 0 o values for GcS and ~ determined in these studies and the 0 o value o f 166 ~; 3 K for (3¢Tc I"~, the a,,~ra~c force constants for these compounds v,-crc calculated. Additionally. literature 0o values for the tin t ~- t 6 and lead w"~chalcogJmides wcrc used to calculate thc avcra~.c force constants o f thcsc compounds. Table 2 fists the Dcbyc t c m l ~ r a t u r ~ , IE)cb~-e frequencies, reduced masses and avcragc force constants for the above I V - V I binary compounds- It can be so~n from Table 2 that the 0t) values d c ~ . ~ with increasing atomic weight o f the chalcogen and o f the metal atoms in this s~ries_ The average force constants o f the metal chalcogenides arc apparently a function o f crystal structure. For the orthorhombic compounds (C;eS, Gc.S~ SnS, SnSc), the average force constant is hi~hcr than for the c,,bic o r rhombohodral structure. The B ~-alues for the orthorhombic compounds are nearly t~vice as large as those for the cubic compounds in this series. The obscr~'ation that the B values for Ge.S and OcS~ arc about cqual sug~csts that thc lower 0 o valuc for ~ is mainly a result o f increased molecular weight and not o f binding differences within the respective solids. Similar conclusions may bc drawn concerning other I V - V [ comp o u n d s with similar B values. Ttm rather large difference in the average force constants bet~n the orthorhombic and cubic IV-VI c o m p o u n d s is probably due to the complex nature o f the orthorhombic structure as compared to thc hi o-.h|y symmetrical NaCl-typc structurc.
The calculation o f ahsoht[e entropies from/teat capacity data T h e Debye function m a y be used to predict the absolutc e n t r o p y o f a c o m p o u n d according to the equation -~-
= 3
(s)
XVe used cqn. (8) to calculatc the absolute entropy o f the ~oermanium chalco~enides at 2--'0 K and the h ~ t capacity functions as measured in these studies to obtain the absolute entropy 3"~.o= for the compounds. From tabulations ~~ ofeqn. (8) and the 0t) valucs o f GcS and GeSc, the abso!utc cntroD- at ?.20 K is 45.2 and :56.5 J K - z mole- ' for GcS and GeSc, respectively_ !ntc~.~rating the heat capacity functions o f Cw.S a n d GeSe from ?.20 to 298 K yields additional e n t r o p y changes o f 14.2 a n d 15.1 J K - ! m o l e - t respectively. T h e absolute
c n t r o p i ~ S~'~s for G e S a n d GeSe arc thus 59.4 ~ 4.0 a n d 71.6 ~: 4.0 J K - ' m o l e - ' rcspeclix~ly. T h e error limits o f ~: 4.0 J K " s mole arc estimated from the 20 K uncertainIy in Ihc 01~ ,,-alucs used to calculate the cntroi~- at "r~__0K. T h e calculation o f S~., s for GcTc is based o n a sorn~t-hat different procedure. Using the 0~, ~ l u c o f 166 ~ 3 K ' * 1he absolute entropy k calculated at 166 K. It is a.~,sumed that o u r G e T c heat capacity funclion [cqn. ( 3 ) ] is ~-a!id from 166~29~ K although the h ~ t capacity xx~ actually measured from "220--4~ K. At 166 K the absolute cxtlropy o f GcTc is 67.8 J K - ~ nsok~ a n d integrating the m_,~_~ured heat c:tpadly -,dd.~ a n additional e n t r o p y chan~e o f 29_7 J IC - s m o l e - * from 166 to 295 K tO ~ e l d 5~.,~s = 97.5 -~ 4.0 J K - s m o l ~ - s for GeTc. A .similar calculalion ba~:d o n the Or, value o f !50 ~ 20 K for G e T e yields ~,~s = 93_7 ~_~4.0 J K - s m o l e - ~ which is m~lhin error l i m i ~ o f the absolute ~rllropy ~-alu¢ oblained using the 0 o x~lluc o f 166 IC. SUMMARY A ~ D CO.'~CI.la~IO.~C~_
As a result o f heat capacity mcasurcmcnls on GeS GcS~ a n d GcTe in the temperature range 220--610 K. 0o ~ l u e s and average force constanls. B. were calculated for the~,e materials a n d com!~-.~cd t o other IV-V! compounds_ It is observed that th~ ma~nitudc o f t lw. B values d c l ~ n d s upon the crystal structure_ T h e absolute entropies at 298 K wcrc calculated to be ~9.4 _-~ 4.0. 7 !.6 .~ 4.0 a n d 97.5 ~ 4.0 J K - a m o l e - t for GeS. GeS~ a n d G c T ~ rcs.ncctK~ly. T h c ~ x~alucs arc in c l o ~ aZ-.rcera~nt w h h absolute ~ r l t r o u ~ cakula(~.'~ independently from K n u d s e . n - t ~ •-aporization studicy,, namely, 58.6 - 6. 70.8 - 8 and 94.6 :~ 8 J K - ~ m o l e - ' for G¢~ '~, Gc.Sc s'~ a n d GeTc ze. rcspccli~'cly. A ~hcrmal effect at 5"0 K o ~ ¢ r v c d in ~be heal capacity m c a ~ u ~ t s o f GcS corrcspondL~ Io a halt in the thermal expansion o f the a- and b-axes observed in high Kempcratur¢ X-ray diffraction ~tudies': o f this c o m p o u n d .
T h e ~ u t h o ~ arc p ~ to acknowledge the support o f this work in part by the National Science F o u n d a t i o n and by t!~ National Aeronautics and Space Administration. REFIERE~CI~ I 2 3 4 5 6 7 &
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